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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Wandering vector multipliers for unitary groups


Authors: Deguang Han and D. Larson
Journal: Trans. Amer. Math. Soc. 353 (2001), 3347-3370
MSC (2000): Primary 46L10, 46L51, 42C40
Published electronically: April 9, 2001
MathSciNet review: 1828609
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Abstract:

A wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system into itself. A special case of unitary system is a discrete unitary group. We prove that for many (and perhaps all) discrete unitary groups, the set of wandering vector multipliers is itself a group. We completely characterize the wandering vector multipliers for abelian and ICC unitary groups. Some characterizations of special wandering vector multipliers are obtained for other cases. In particular, there are simple characterizations for diagonal and permutation wandering vector multipliers. Similar results remain valid for irrational rotation unitary systems. We also obtain some results concerning the wandering vector multipliers for those unitary systems which are the ordered products of two unitary groups. There are applications to wavelet systems.


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Additional Information

Deguang Han
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816-1364
Email: dhan@pegasus.cc.ucf.edu

D. Larson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: David.Larson@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02795-7
PII: S 0002-9947(01)02795-7
Keywords: Unitary system, wandering vector, wandering vector multiplier, von Neumann algebra, wavelet system
Received by editor(s): February 5, 1998
Published electronically: April 9, 2001
Additional Notes: (DH) Participant, Workshop in Linear Analysis and Probability, Texas A&M University
(DL) This work was partially supported by NSF
Article copyright: © Copyright 2001 American Mathematical Society